What are the purposes of autoencoders?
It is important to think about what sort of patterns in the data are being represented. 

Suppose that you have a dataset of greyscale images, such that every image is a uniform intensity. As a human brain you'd realise that every element in this dataset can be described in terms of a single numeric parameter, which is that intensity value. This is something that PCA would work fine for, because each of the dimensions (we can think of each pixel as a different dimension) is perfectly linearly correlated. 

Suppose instead that you have a dataset of black and white 128x128px bitmap images of centred circles. As a human brain you'd quickly realise that every element in this dataset can be fully described by a single numeric parameter, which is the radius of the circle. That is a very impressive level of reduction from 16384 binary dimensions, and perhaps more importantly it's a semantically meaningful property of the data. However, PCA probably won't be able to find that pattern.

Your question was "Why can't we simply use PCA, if the purpose is dimensionality reduction?" The simple answer is that PCA is the simplest tool for dimensionality reduction, but it can miss a lot of relationships that more powerful techniques such as autoencoders might find.